1. Field of the Invention
The invention relates to fractional carrier frequency offset estimators and methods of estimating fractional carrier frequency offset between receiver and transmitter. The invention may be particularly applied in Orthogonal Frequency Division Multiplexing (OFDM) related systems including Orthogonal Frequency Division Multiple Access (OFDMA) system, such as WiMAX system.
2. Description of the Related Art
FIG. 1 illustrates a wireless communication system 100, comprising a transmitter 102 and a receiver 104. In the transmitter 102, a signal s(t) is mixed with a signal ej2πftxl and is then broadcast by an antenna 106. The emitted broadcast signal is received by an antenna 108 of the receiver 104. In the receiver 104, the signal received by the antenna 108 is mixed with a signal of e−j2πfrxf to generate a received signal r(t), wherein r(t)=s(t)·ej2πftxt·e−j2πfrxl=s(t)·ej2π(ftx−frx)t=s(t)·ej2πfΔf, where fΔ represents carrier frequency offset between the transmitter 102 and the receiver 104. After normalizing the carrier frequency fΔ to the subcarrier spacing of the system, the carrier frequency offset fΔ is divided into integral portion fint and fractional portion ffrac, wherein fΔ=fint+ffrac. In a conventional technique, such as that disclosed in U.S. Pat. No. 5,732,113, the fractional carrier frequency offset between the transmitter and receiver (ffrac) is estimated by evaluating a delay correlation based on the first and second preamble repetitions of the received signal r(t) and multiplying the phase of the delay correlation by a predetermined value.
The preamble of a received signal in a WLAN (Wireless Local Area Network, IEEE 802.11a) system is shown in FIG. 2. The preamble comprises a short preamble and a long preamble. The short preamble comprises ten identical preamble repetitions A1˜A10, and the long preamble comprises two identical preamble repetitions B1 and B2. In the described conventional technique, the fractional carrier frequency offset (ffrac) can be estimated by using any two repetitions (e.g., A1 and A2) of the short preamble of a received signal r(t). Based on the sampled data in the first and second preamble repetitions (A1 and A2), a delay correlation, z12, is obtained by the formula:
            z      12        =                  ∑                  n          =          0                          N          -          1                    ⁢                          ⁢                        r          n                ·                  r                      (                          n              +              D                        )                    *                      ,where N represents the accumulation samples included in one preamble repetition, D represents the delay between the identical samples of the two preamble repetitions (e.g., A1 and A2), and ‘*’ represents a complex conjugate operation. The sample duration of the received signal r(t) is T. Because 0≦n≦(N−1), rn represents samples in the first preamble repetition A1, rn+D represents samples in the second preamble repetition A2. FIG. 1 shows—r(t) equals s(t)·ej2πfΔt—rn is sn·ej2πfΔnTs and rn+D is sn+D·ej2πfΔ(n+D)Ts. When noise and frequency disturbance are not present in the communication system, sn equals sn+D. The delay correlation, z12, can be further simplified as the following:
                              z          12                =                                            ∑                              n                =                0                                            N                -                1                                      ⁢                                                  ⁢                                          s                n                            ·                              ⅇ                                  j                  ⁢                                                                          ⁢                  2                  ⁢                  π                  ⁢                                                                          ⁢                                      f                    Δ                                    ⁢                                      nT                    s                                                              ·                                                (                                                            s                                              n                        +                        D                                                              ·                                          ⅇ                                              j                        ⁢                                                                                                  ⁢                        2                        ⁢                        π                        ⁢                                                                                                  ⁢                                                                              f                            Δ                                                    ⁡                                                      (                                                          n                              +                              D                                                        )                                                                          ⁢                                                  T                          s                                                                                                      )                                *                                              =                                    ⅇ                                                -                  j                                ⁢                                                                  ⁢                2                ⁢                π                ⁢                                                                  ⁢                                  f                  Δ                                ⁢                                  DT                  s                                                      ⁢                                          ∑                                  n                  =                  0                                                  N                  -                  1                                            ⁢                                                          ⁢                                                                                                              s                      n                                                                            2                                .                                                                        (                  eq          .                                          ⁢          1                )            Based on the phase of the delay correlation (∠z12), the fractional carrier frequency offset between the transmitter and receiver can be determined by multiplying the phase of the delay correlation (∠z12) by −1/(2πDTs), thus, when the first and second preamble repetitions are exactly identical, the fractional carrier frequency offset is estimated by the formula:
                              f          frac                =                              -                          1                              2                ⁢                π                ⁢                                                                  ⁢                                  DT                  s                                                              ⁢          ∠          ⁢                                          ⁢                      z            12                                              (                  eq          .                                          ⁢          2                )            
The IEEE 802.16e standard, commonly referred to as the WiMAX (Worldwide Interoperability for Microwave Access), its preamble has three-repetition property. Thus, the delay correlation operation can be applied. The 3-repetition preamble is designed for 3-sector cellular planning. FIG. 3 shows the cellular planning of a WiMAX system. Each cell is divided into three sectors; sector 1, sector 2 and sector 3. In sector 1, a delay correlation, z12, based on the first and second preamble repetitions of a received signal, is C1·e−j2πfΔDTs·ejφ1 because the second preamble repetition is not exactly identical to the first preamble repetition. Compared with equation 1, the delay correlation z12 of a signal in sector 1 has a phase rotation of φ1. Similarly, delay correlations of signals in sector 2 and sector 3 have phase rotations of φ2 and φ3, respectively. Thus, an improved method for fractional carrier frequency offset estimation is desirable.